Having armor be volume limited is weird, but OK it's your world. Maybe they have some kind of novel power source?
Normally when weight is critical, the best armor uses extremely hard materials on the outer surface (ceramic seems to be the state of the art), then there is an air gap, then a material with a high tensile strength to weight ratio (kevlar, titanium, or steel depending on the application), and lastly there is some kind of a spall liner usually made from kevlar fabric. The hard outer surface breaks the projectile into pieces and slows those pieces down. The middle layer absorbs the remaining kinetic energy of the now shattered projectile. Finally, the spall liner catches fragments of the middle layer of armor which break loose at high velocity, ideally without catching fire (thus kevlar rather than UHMWPE). This tends to use up a lot of space though.
There is another class of armor called reactive armor which consists of a sandwich of two steel plates with plastic explosive in the middle. This is mainly useful for resisting shaped charges, but I think any shaped charge weapon is going to be out of your league.
If weight is of no consequence, then extremely dense materials become appealing. I think you will find very few examples since this is essentially never the case, but some tank armors incorporate depleted uranium in the above layer sandwich. Ceramic is still ideal for the outer layer, but you would likely want to use tungsten carbide because it's extremely hard and extremely dense. You would likely back this with depleted uranium or a high strength steel.
.50 caliber ammunition comes in a wide variety of types. https://en.wikipedia.org/wiki/.50_BMG I couldn't find the video you reference, but it likely involved regular ball ammunition. (Copper over a steel core.) APDS (armor piercing discarding sabot) uses a small, very pointy tungsten rod wrapped in a plastic sleeve (the sabot). When fired, the sabot breaks off, leaving the tungsten rod to impact the target on its own. Penetrating power of a bullet tends to be closely related to the pounds per square inch it can exert on the target. Since tungsten is far denser than steel, a tungsten bullet with the same weight and and length as a steel bullet will penetrate far more armor. The M903 APDS round will reportedly penetrate 34mm of rolled homogeneous steel armor (the default armor plate) at 500 meters. My point is that 30mm of the best armor you can get might very well resist a single shot of .50 cal ball, but would likely succumb to several shots of .50 APDS.
side question 1: Pretty much all armor is wrecked at the point where the bullet contacts it. Ceramic armors are created as many individual blocks and the entire block shatters when hit. If accurate repeated fire or extremely high volumes of fire result in multiple bullet hits to the same location, all armors will eventually fail.
side question 2: More armor means better protection. That said, another option would be to just add a few redundant electronic boxes which take over when the first one is damaged. This is standard practice in spacecraft. Computers are tiny, light, and fairly cheap. Armor is big, very heavy, and expensive. A really clever drone might even use multiple processors in parallel in order to process a lot of data really quickly in the middle of combat, then as those processors become destroyed it might switch to a redundancy mode, making its behavior more sluggish but stubborn. This might add some drama to a scene involving trying to kill one of these drones?